Seasonal variation in daily activity patterns of snow leopards and their prey

The daily and seasonal activity patterns of snow leopards (Panthera uncia) are poorly understood, limiting our ecological understanding and hampering our ability to mitigate threats such as climate change and retaliatory killing in response to livestock predation. We fitted GPS-collars with activity loggers to snow leopards, Siberian ibex (Capra sibirica: their main prey), and domestic goats (Capra hircus: common livestock prey) in Mongolia between 2009 and 2020. Snow leopards were facultatively nocturnal with season-specific crepuscular activity peaks: seasonal activity shifted towards night-sunrise during summer, and day-sunset in winter. Snow leopard activity was in contrast to their prey, which were consistently diurnal. We interpret these results in relation to: (1) darkness as concealment for snow leopards when stalking in an open landscape (nocturnal activity), (2) low-intermediate light preferred for predatory ambush in steep rocky terrain (dawn and dusk activity), and (3) seasonal activity adjustments to facilitate thermoregulation in an extreme environment. These patterns suggest that to minimise human-wildlife conflict, livestock should be corralled at night and dawn in summer, and dusk in winter. It is likely that climate change will intensify seasonal effects on the snow leopard's daily temporal niche for thermoregulation in the future.

Because these GLMMs were formulated in a Bayesian framework, we performed model checks for convergence of the chains (by visualizing the stability of individual chains and the mixing of multiple chains for the final estimation), and the appropriateness of the likelihood distribution and model formulation by undertaking poster predictive checks where we simulated data from the model and compared the means and variances to the raw data. In all cases the Bayes P values were between 0.4 & 0.6 (ideal range is between 0.1 & 0.9). These were implemented in JAGS (Plummer 2007) run from R (R Core Team 2019).
GAMM models for snow leopard activity during different time periods We ran two types of GAMMs on the accelerometer activity data from the snow leopards to examine seasonal changes in general activity during four periods during the 24-hour cycle: dawn, day, dusk and night. For all GAMMs we used month as a fixed smoothing term to explain variation in the activity rate and included the individual ID as a random effect in the gamm() function from the 'mgcv' package in R.
The general model structure for the activity data structured as a binary variable to look at patterns of activity versus inactivity (i.e. the proportion of time active as defined as accelerometer values of <28 versus >28) was: The general model structure for the activity data when only looking at activity when the animal was not resting (i.e. accelerometer values of >28; see Nygren, E. 2015. Activity patterns of snow leopards (Panthera uncia) at their kill sites. Master's thesis, Swedish University of Agricultural Sciences, Uppsala, Sweden) was: For activity data collected at night we also estimated lunar illumination based on moonrise and phase, and used GAMs to examine whether motion activity in snow leopards was related to lunar illumination during the night periods when the moon was above the horizon (as a smoothed fixed effect).
Supplementary Methods B: Converting the 5-hour GPS movement data to hourly movement data Because the snow leopard GPS-movement data was taken 5-hourly, we used these data to create an average movement observation for each of the 5 hours that the period encompassed (i.e. 1/5 of the total movement was assigned to each period hour). To check that these data would capture the general variation in daily activity patterns we were interested in, we simulated similar data and then 'sampled' this total movement every 5 hours and back transformed it into hourly observations. This demonstrated that if many samples are taken, this method of estimation largely preserves the original pattern of daily variation, especially when patterns shift between periods of stable activity (Fig. A). However, when there are sudden changes of large magnitude or short-term peaks and troughs in the activity patterns, these effects may be 'smoothed' in appearance (Fig. B) or 'blunted' in their magnitude (Fig. C).

Fig. A:
Comparing the temporal patterns of simulated activity data collected hourly (in black) and the same data if collected 5-hourly and then 'back transformed' into hourly data by assigning 1/5 of the 5-hourly measurements to the 5 hourly periods that comprised that 5-hourly measurement (see methods) This code was used to probabilistically sample from the shape of the distribution that best approximated the daily activity patterns for the group we were interested in (i.e. mean estimates of activity in relation to 'sun times' from the raw data. The result of the 10,000 MCMC samples generated from this algorithm is that they could then be used to generate activity density plots and between-group overlap calculations and plots using the 'overlap' package in R (overlapPlot and overlapEst functions; Ridout & Linkie 2009). This sampling method also allows proportional estimates of total activity during different time periods, in the same way that probabilities can be calculated from Bayesian posterior distributions. #read in the data data<-read.csv("suntime_activity_data.csv") #here there are two columns data$sun.times #where the observation time of the acvtivity is recorded in 'sun.time' (see Nouvellet et al 2011) data$activity #the activity level (either movement or motion) as recorded by the GPS collar for that corresponding 'sun.time' period #create a series of 60 activity means spread across the range of suntimes spanning the day #can choose as many as you want, but 60 seems to be a good compromise between daily pattern detail and data availability at each break point  S1. Histogram of the raw snow leopard GPS-movement data showing the frequency of observed snow leopard movements related to the straight-line distance (displacement) they moved from one GPS position to the next (5 hours later). The left panel (a) shows all the data, but because of the extreme number of points close to zero, the rest of the data are difficult to see at that scale. The right panel (b) is the same figure, but the y-axis has been truncated at 300 to better show the patterns of the data distribution for distances greater than 50m.  . The relative proportion of snow leopard activity across the 24-hour cycle for males (blue) and females (red) for the two types of activity data collected from GPS-collars (a = GPS displacement movement data; b = accelerometer motion activity data). The activity densities on the y-axis have no absolute meaning, but rather are relative measures of probability density calculated from the raw movement data. The time of all observations has been standardized along the x-axis using 'sun-times'; where the time of observation on each day is calibrated to sunrise, solar-noon (midday) and sunset. These overlap plots show the activity overlap between males and female (grey) and highlight periods when males or females have greater activity (blue or red shaded, respectively).

Fig. S6.
Prediction of snow leopard accelerometer activity level based on the fraction of the moon being illuminated (where 0 = no moon, 1 = full moon) from a GAMM using moon fraction as a fixed effect smoother and individual ID as a random effect. The line is the predicted mean and the shaded area is the standard error of the prediction.